Multiplying through by , we have
So
Factorizing we have
Solving we have  of
If
sine
 hn sha inle
1e

Let .
Factorizing we have

So  or

Also  or  is not real

.
We can express the given equation thus.
 
Now let
Factorizing we have
Hence  or
,
If
If  then  i.e.  is undefined

Simplifying the equation we have

Let  then
Dividing through by 2 the common factor to the terms,

Factorizing we have
Hence  or
But , so  or
Therefore  or  i.e.  is undefined.

We rewrite the equation thus:

Let  then
Factorizing we have

 or
But
Hence  or
If , then
Also if  (  is undefined or  is notareal number)

We express the equation as

Let
Factorising we have
 or
 or
But , so  or
Considering
We apply logarithms thus


If  then,  which means no real number satishes the equation.

, then
Factorising, we have

 or
But  or   or
By comparison of powers we have  or

(i)

(ii)
(iii)

a)

From the table above the last two columns are identical. Hence ∼p∧∼q and ∼(p∨q) are logically equivalent
b)

The last two columns of the table above are identical. Hence ∼(p∧q) and ∼p∨∼q are logically equivalent

a) No student is present.
b) Albert will not do Mathematics and Albert will not do Physics.
c) The teacher is not teaching or the students are not listening.

d) She is a student and she will not write the exam.
e) For all